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Mathematical Analysis
Mathematical analysis is, simply put, the study of limits and how they can be manipulated. Starting with an exhaustive study of sets, mathematical analysis then continues on to the rigorous development of calculus, differential equations, model theory, and topology. Topics including real and complex analysis, differential equations and vector calculus can be discussed in this category.
2,575 Questions
How can you reduce zero point zero zero two over a thousand?
0.002 = 2/1000 = 1/500
0.002/1000 = 2/1000000 = 1/500000
If, as you approach the variable from either side, the value of the function increases without bound, then the limit of the function is infinity. More formally, the limit of a function, f(x) is infinity at x = z if, given any large number N you can find a number d such that f(x) > N for all x such that |x - z| < d.
In other words, you can always find an immediate neighbourhood of z, such that the value of the function is larger than any number you care to name.
There are several possible scenarios in which a limit may not exist. A common situation is when the limits are different depending on which direction you approach z from. For example, consider f(x) = 1/x and z = 0.
If you approach z from the positive side, then f(x) can be made larger than any large positive number: limit = + infinity. On the other hand, if you approach z from the negative side, f(z) can be made smaller than any negative number: limit = - infinity.
The limits need not be infinite. You could have a function defined as follows:
f(x) = 0 for 0 <= x < 1
f(x) = 1 for x >= 1
Approaching 1 from "below", the limit of f(x) is 0 while from "above", you get f(x) = 1. This kind of function - an indicator function- is quite common. For example, the presence of a current in a circuit if the power is switched on at time x = 1.
How do you solve 5xy plus 7xsquared - 12y when x equals 2 y equals 1?
In the given expression you replace x by 2 and y by 1.
Thus 5xy + 7x2 - 12y = 5*x*y + 7*x2 - 12*y
= 5*2*1 + 7*22 - 12*1 = 10 + 28 - 12 = 26
if two signal input fed into circuit and gating one output
At any given time in hours after the family departs, the distance they have travelled will be 60t, while at the same time, the moving van will have covered a distance of 55(t + 1). The family will catch up when these two times are equal, or when 60t = 55(t + 1), or 60t - 55t = 55, or 5t = 55, or t = 55/5 hours = 11 hours.
How much greater is 4 to the power of 2 than 4 to the power of negative 2?
4 to the power of 2 is 42 = 16
4 to the power of negative 2 is 4-2 = 1/42 = 1/16
As far as "how much greater" - that depends on what you mean
If you mean what is the size of the difference...
16 - 1/16 = 15 15/16 = 15.9375 so 4² is 15.9375 greater than 1/4²
If you mean the ratio...
42/4-2 = 44 = 256 so 42 is 256 times the size of 4-2 or 255 times bigger
(i.e. 42 = 4-2 + 255·4-2)
What does the number 0408163245576318222527346277 mean?
It does not mean anything specifically. In a particular context it may have some meaning but you have chosen not to share that context with us.
What if you fell 4 classes in 9 grade?
If you fail 4 classes you will still be classified as a 9th grader.
What numbers add to give you 8 but multiply to give you 36?
4 + 2i*sqrt(5) and 4 - 2i*sqrt(5)
[where i is the square root of -1]
Given a+b=8, we have b=8-a.
Given ab = 36, we can substitute b=8-a to get a(8-a) = 36, or
a2 - 8a + 36 = 0
Using the quadratic formula gives the two possible answers, which accounts for the fact that a and b can be switched without affecting the problem.
How many kilometers are there in 820 meters?
There are 1000 metres in one kilometre. Therefore, 820 metres is equal to 820/1000 = 0.82 kilometres.
How do you compare one ratio against another ratio?
You divide them. For instance, to compare 1:3 against 3:5, treat them as fractions (1/3 and 3/5) and divide, in this case getting 5/9, which says that 1:3 is slightly more than half of 3:5. Remember that you can divide fractions by inverting one of them and multiplying - 1/3 divided by 3/5 is the same as 1/3 multiplied by 5/3.
Why is du infinitely small in calculus?
du refers to a differential part of u, which is infinitely small.
Why do we take a limit in math?
There are situations in mathematics where the value of a function is not defined for some value of the argument but you can get closer and closer to a fixed value. In such cases a limit may be the appropriate solution for finding an answer.
